Solve for $x$ and $y$ using elimination. ${-2x-2y = -20}$ ${-5x+2y = -36}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-7x = -56$ $\dfrac{-7x}{{-7}} = \dfrac{-56}{{-7}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-2x-2y = -20}\thinspace$ to find $y$ ${-2}{(8)}{ - 2y = -20}$ $-16-2y = -20$ $-16{+16} - 2y = -20{+16}$ $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {-5x+2y = -36}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + 2y = -36}$ ${y = 2}$